Zero divisor graphs of commutative graded rings

Cooper, Katherine; Johnson, Brian

doi:10.2140/involve.2018.11.283

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Zero divisor graphs of commutative graded rings

Katherine Cooper and Brian Johnson

Vol. 11 (2018), No. 2, 283–295

DOI: 10.2140/involve.2018.11.283

Abstract

We study a natural generalization of the zero divisor graph introduced by Anderson and Livingston to commutative rings graded by abelian groups, considering only homogeneous zero divisors. We develop a basic theory for graded zero divisor graphs and present many examples. Finally, we examine classes of graphs that are realizable as graded zero divisor graphs and close with some open questions.

Keywords

graded ring, zero divisor graph

Mathematical Subject Classification 2010

Primary: 05C25, 13A02

Milestones

Received: 30 September 2016

Revised: 17 March 2017

Accepted: 23 March 2017

Published: 17 September 2017

Communicated by Scott T. Chapman

Authors

Katherine Cooper
Department of Mathematics University of Kentucky Lexington, KY United States

Brian Johnson
Department of Mathematics Florida Gulf Coast University Fort Myers, FL United States

Vol. 11, No. 2, 2018